Abstract. We present a paraUel variant of the inexact Newton algorithm that uses the Krylov multisplitting algorithm (KMS) to compute the approxrmate Newton direction. The algorithm can be used for solving unconstrained optimization problems or systems of nonlinear equations. The KMS algorithm is a more efficient paraUel implementation of Krylov subspace methods (GMRES, Arnoldi, etc.) with multisplitting preconditioners. The work of the KMS algorithm is divided into the multisplitting tasks and a direction forrning task. There is a great deal of paraUelism within each task and the number of synchronization points between the tasks is greatly reduced. We study the local and global convergence properties of the algorithm and present results of numerical examples on a sequential computer. (Also cross-referenced as UMIACS-TR-93-71)